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Search found 3365 results on 135 pages for 'math'.

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• how to subtract circle from an arbitrary polygon

  - by George

  Given an arbitary polygon with vertices stored in either clockwise/counterclockwise fashion (depicted as a black rectangle in the diagram), I need to be able to subtract an arbitrary number of circles (in red on the diagram) from that polygon. Removing a circle could possibly split the polygon into two seperate polygons (as depicted by the second line in the diagram). I'm not sure where to start. http://www.freeimagehosting.net/image.php?89a0276d9d.jpg

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• Rewrite probabilities as boolean algebra

  - by Magsol

  I'm given three binary random variables: X, Y, and Z. I'm also given the following: P(Z | X) P(Z | Y) P(X) P(Y) I'm then supposed to determine whether or not it is possible to find P(Z | Y, X). I've tried rewriting the solution in the form of Bayes' Theorem and have gotten nowhere. Given that these are boolean random variables, is it possible to rewrite the system in terms of boolean algebra? I understand that the conditionals can be mapped to boolean implications (x -> y, or !x + y), but I'm unsure how this would translate in terms of the overall problem I'm trying to solve. (yes, this is a homework problem, but here I'm much more interested in how to formally solve this problem than what the solution is...I also figured this question would be entirely too simple for MathOverflow)

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• Divide not returning the decimal value i expect.

  - by gtas

  if you divide 2 / 3 should return 0,66666666666666667 instead i get in double value type 0.0 in decimal 0. My purpose is to divide even (e.g. 2 / 3) and round to 1 always to the nearest. Any Help?

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• KD-Trees and missing values (vector comparison)

  - by labratmatt

  I have a system that stores vectors and allows a user to find the n most similar vectors to the user's query vector. That is, a user submits a vector (I call it a query vector) and my system spits out "here are the n most similar vectors." I generate the similar vectors using a KD-Tree and everything works well, but I want to do more. I want to present a list of the n most similar vectors even if the user doesn't submit a complete vector (a vector with missing values). That is, if a user submits a vector with three dimensions, I still want to find the n nearest vectors (stored vectors are of 11 dimensions) I have stored. I have a couple of obvious solutions, but I'm not sure either one seem very good: Create multiple KD-Trees each built using the most popular subset of dimensions a user will search for. That is, if a user submits a query vector of thee dimensions, x, y, z, I match that query to my already built KD-Tree which only contains vectors of three dimensions, x, y, z. Ignore KD-Trees when a user submits a query vector with missing values and compare the query vector to the vectors (stored in a table in a DB) one by one using something like a dot product. This has to be a common problem, any suggestions? Thanks for the help.

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• What area of Mathematics is most useful to general programming knowledge?

  - by chustar

  I need to take elective mathematics classes and I was wondering which ones have been most helpful to programmers on stackoverflow. I'm interested in taking topology because of http://abstrusegoose.com/254 but was wondering what would be helpful to know as far as (general purpose) programming goes.

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• reflection paths between points in2d

  - by Chris H

  Just wondering if there was a nice (already implemented/documented) algorithm to do the following Given any shape (without crossing edges) and two points inside that shape, compute all the paths between the two points such that all reflections are perfect reflections. The path lengths should be limited to a certain length otherwise there are infinite solutions. I'm not interested in just shooting out rays to try to guess how close I can get, I'm interested in algorithms that can do it perfectly. Search based, not guess/improvement based.

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• Check if BigInteger is not a perfect square

  - by Ender

  I have a BigInteger value, let's say it is 282 and is inside the variable x. I now want to write a while loop that states: while b2 isn't a perfect square: a ? a + 1 b2 ? a*a - N endwhile How would I do such a thing using BigInteger? EDIT: The purpose for this is so I can write this method. As the article states one must check if b2 is not square.

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• calculating parameters for defining subsections of quadratic bezier curves

  - by jedierikb

  I have a quadratic bezier curve described as (startX, startY) to (anchorX, anchorY) and using a control point(controlX, controlY). I have two questions: (1) I want to determine y points on that curve based on an x point. (2) Then, given two intermediary points on that bezier curve, I want to know the 6 parameters needed to create that mini-bezier curve.

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• Fast 4x4 matrix multiplication in Java with NIO float buffers

  - by kayahr

  I know there are LOT of questions like that but I can't find one specific to my situation. I have 4x4 matrices implemented as NIO float buffers (These matrices are used for OpenGL). Now I want to implement a multiply method which multiplies Matrix A with Matrix B and stores the result in Matrix C. So the code may look like this: class Matrix4f { private FloatBuffer buffer = FloatBuffer.allocate(16); public Matrix4f multiply(Matrix4f matrix2, Matrix4f result) { {{{result = this * matrix2}}} <-- I need this code return result; } } What is the fastest possible code to do this multiplication? Some OpenGL implementations (Like the OpenGL ES stuff in Android) provide native code for this but others doesn't. So I want to provide a generic multiplication method for these implementations.

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• Divide and conquer method to compute roots

  - by hellsoul153

  Hello, Knowing that we can use Divide-and-Conquer algorithm to compute large exponents, for exemple 2 exp 100 = 2 exp(50) * 2 exp(50), which is quite more efficient, is this method efficient using roots ? For exemple 2 exp (1/100) = (2 exp(1/50)) exp(1/50) ?

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• How do I get a decimal value when using the division operator in Python?

  - by Ray Vega

  For example, the standard division symbol '/' rounds to zero: >>> 4 / 100 0 However, I want it to return 0.04. What do I use?

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• Need some help understanding this problem about maximizing graph connectivity

  - by Legend

  I was wondering if someone could help me understand this problem. I prepared a small diagram because it is much easier to explain it visually. Problem I am trying to solve: 1. Constructing the dependency graph Given the connectivity of the graph and a metric that determines how well a node depends on the other, order the dependencies. For instance, I could put in a few rules saying that node 3 depends on node 4 node 2 depends on node 3 node 3 depends on node 5 But because the final rule is not "valuable" (again based on the same metric), I will not add the rule to my system. 2. Execute the request order Once I built a dependency graph, execute the list in an order that maximizes the final connectivity. I am not sure if this is a really a problem but I somehow have a feeling that there might exist more than one order in which case, it is required to choose the best order. First and foremost, I am wondering if I constructed the problem correctly and if I should be aware of any corner cases. Secondly, is there a closely related algorithm that I can look at? Currently, I am thinking of something like Feedback Arc Set or the Secretary Problem but I am a little confused at the moment. Any suggestions? PS: I am a little confused about the problem myself so please don't flame on me for that. If any clarifications are needed, I will try to update the question.

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• draw an arc given 3 points in SWT

  - by Ahmed Kotb

  iam using the swt java library and iam having a problem. the gc draw arc method takes the following arguments GC.drawArc(int x, int y, int width, int height, int startAngle, int endAngle); but i want to be able to draw the arc using 3 arguments : the source ,destination and control points. is there any formula to convert between those parameters ? QuadCurve2D class do exactly what i want but it is not AWT not swt ...and i tried to use java2d under swt but it was very slow .... any solutions ?

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• Tangent of a parametric discrete curve

  - by gregseth

  I have a parametric curve, say two vectors of doubles where the parameter is the index, and I have to calculate the angle of the tangent to this curve at any given point (index). Any suggestion or link about how to do that? Thanks.

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• An algorithm for converting a base-10 number to a base-N number.

  - by roja

  Guys, I am looking for a way to convert a base-10 number into a base-N number where N can be large. Specifically i am looking at converting to base-85 and back again. Does anyone know a simple algorithm to perform the conversion? Ideally it would provide something like: to_radix(83992, 85) - [11, 53, 12] Any ideas are appreciated! Roja

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• Fibonacci sequence subroutine returning one digit too high...PERL

  - by beProactive

  #!/usr/bin/perl -w use strict; sub fib { my($num) = @_; #give $num to input array return(1) if ($num<=1); #termination condition return($num = &fib($num-1) + &fib($num-2)); #should return sum of first "n" terms in the fibonacci sequence } print &fib(7)."\n"; #should output 20 This subroutine should be outputting a summation of the first "x" amount of terms, as specified by the argument to the sub. However, it's one too high. Does this have something to do with the recursion? Thanks.

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• Choosing circle radius to fully fill a rectangle

  - by Andy

  Hi, the pixman image library can draw radial color gradients between two circles. I'd like the radial gradient to fill a rectangular area defined by "width" and "height" completely. Now my question, how should I choose the radius of the outer circle? My current parameters are the following: A) inner circle (start of gradient) center pointer of inner circle: (width*0.5|height*0.5) radius of inner circle: 1 color: black B) outer circle (end of gradient) center pointer of outer circle: (width*0.5|height*0.5) radius of outer circle: ??? color: white How should I choose the radius of the outer circle to make sure that the outer circle will entirely fill my bounding rectangle defined by width*height. There shall be no empty areas in the corners, the area shall be completely covered by the circle. In other words, the bounding rectangle width,height must fit entirely into the outer circle. Choosing outer_radius = max(width, height) * 0.5 as the radius for the outer circle is obviously not enough. It must be bigger, but how much bigger? Thanks!

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• how to determine base of a number?

  - by evil.coder

  Given a integer number and its reresentation in some arbitrary number system. The purpose is to find the base of the number system. For example, number is 10 and representation is 000010, then the base should be 10. Another example: number 21 representation is 0010101 then base is 2. One more example is: number is 6 and representation os 10100 then base is sqrt(2). Does anyone have any idea how to solve such problem?

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• Drawing Directed Acyclic Graphs: Minimizing edge crossing?

  - by Robert Fraser

  Laying out the verticies in a DAG in a tree form (i.e. verticies with no in-edges on top, verticies dependent only on those on the next level, etc.) is rather simple without graph drawing algorithms such as Efficient Sugimiya. However, is there a simple algorithm to do this that minimizes edge crossing? (For some graphs, it may be impossible to completely eliminate edge crossing.) A picture says a thousand words, so is there an algorithm that would suggest: instead of: EDIT: As the picture suggests, a vertex's inputs are always on top and outputs are always below, which is another barrier to just pasting in an existing layout algorithm.

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• Power function fit to data set

  - by czerasz

  I have a set of data (in ArrayCollection) and I need to fit a power function { f(x)= B + x^alpha } to it, before display in LineChart. As result I need the alpha and B paremeter. How to do this with Flex?

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• Sparse quadratic program solver

  - by Jacob

  This great SO answer points to a good sparse solver, but I've got constraints on x (for Ax = b) such that each element in x is >=0 an <=N. The first thing which comes to mind is an QP solver for large sparse matrices. Also, A is huge (around 2e6x2e6) but very sparse with <=4 elements per row. Any ideas/recommendations?

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• Finding the intersection of two vector equations.

  - by Matthew Mitchell

  I've been trying to solve this and I found an equation that gives the possibility of zero division errors. Not the best thing: v1 = (a,b) v2 = (c,d) d1 = (e,f) d2 = (h,i) l1: v1 + ?d1 l2: v2 + µd2 Equation to find vector intersection of l1 and l2 programatically by re-arranging for lambda. (a,b) + ?(e,f) = (c,d) + µ(h,i) a + ?e = c + µh b +?f = d + µi µh = a + ?e - c µi = b +?f - d µ = (a + ?e - c)/h µ = (b +?f - d)/i (a + ?e - c)/h = (b +?f - d)/i a/h + ?e/h - c/h = b/i +?f/i - d/i ?e/h - ?f/i = (b/i - d/i) - (a/h - c/h) ?(e/h - f/i) = (b - d)/i - (a - c)/h ? = ((b - d)/i - (a - c)/h)/(e/h - f/i) Intersection vector = (a + ?e,b + ?f) Not sure if it would even work in some cases. I haven't tested it. I need to know how to do this for values as in that example a-i. Thank you.

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• Solving the water jug problem

  - by Amit

  While reading through some lecture notes on preliminary number theory, I came across the solution to water jug problem (with two jugs) which is summed as thus: Using the property of the G.C.D of two numbers that GCD(a,b) is the smallest possible linear combination of a and b, and hence a certain quantity Q is only measurable by the 2 jugs, iff Q is a n*GCD(a,b), since Q=sA + tB, where: n = a positive integer A = capacity of jug A B= capacity of jug B And, then the method to the solution is discussed Another model of the solution is to model the various states as a state-space search problem as often resorted to in Artificial Intelligence. My question is: What other known methods exist which models the solution, and how? Google didn't throw up much.

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• BigInteger.pow(BigInteger) ?

  - by PeterW

  I'm playing with numbers in Java, and want to see how big a number I can make. It is my understanding that BigInteger can hold a number of infinite size, so long as my computer has enough Memory to hold such a number, correct? My problem is that BigInteger.pow accepts only an int, not another BigInteger, which means I can only use a number up to 2,147,483,647 as the exponent. Is it possible to use the BigInteger class as such? BigInteger.pow(BigInteger) Thanks.

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• Diagonal of polygon is inside or outside?

  - by Himadri

  I have three consecutive points of polygon, say p1,p2,p3. Now I wanted to know whether the orthogonal between p1 and p3 is inside the polygon or outside the polygon. I am doing it by taking three vectors v1,v2 and v3. And the point before the point p1 in polygon say p0. v1 = (p0 - p1) v2 = (p2 - p1) v3 = (p3 - p1) With reference to this question, I am using the method shown in the accepted answer of that question. It is only for counterclockwise. What if my points are clockwise. I am also knowing my whole polygon is clockwise or counterclockwise. And accordingly I select the vectors v1 and v2. But still I am getting some problem. I am showing one case where I am getting problem. This polygon is counterclockwise. and It is starting from the origin of v1 and v2.

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